Joint probability density function

Thread Starter

boks

Joined Oct 10, 2008
218
Let X, Y, and Z have the joint probability density function

f(x, y, z) = kx(y^2)z, for x>0, y<1, 0<z<2

find k


\(\int_{0}^{2}\int_{- \infty}^{1}\int_{0}^{\infty}kxy^2z dx dy dz\)

This integral should equal 1. Is my procedure correct so far? I don't manage to solve the integral...
 
Last edited:

steveb

Joined Jul 3, 2008
2,436
Let X, Y, and Z have the joint probability density function

f(x, y, z) = kx(y^2)z, for x>0, y<1, 0<z<2

find k


\(\int_{0}^{2}\int_{- \infty}^{1}\int_{0}^{\infty}kxy^2z dx dy dz\)

This integral should equal 1. Is my procedure correct so far? I don't manage to solve the integral...
That looks correct assuming that the joint probability function is zero everywhere else. You didn't say that explicitly, but it seems implied.

You should have no trouble evaluating that integral.
 
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